Short description

FE2TI is a combination of the FE2 method with hybrid domain decomposition/multigrid solvers. The FE2 method is a computational micro-macro scale bridging approach directly incorporating micromechanics in macroscopic simulations. In this approach, a microscopic boundary value problem based on the definition of a representative volume element (RVE) is solved at each macroscopic Gauß integration point. Then, volumetric averages of microscopic stress distributions are returned to the macroscopic level, which replaces a phenomenological material law at the macro scale. The microscopic problems are thus coupled through the macroscopic problem. On the RVEs nonlinear implicit structural mechanics problems have to be solved. We are applying the FETI-DP (Finite Element Tearing and Interconnecting) method as a solver on the RVEs. Nonoverlapping domain decomposition methods of the FETI type are well established solution methods in implicit structural mechanics. A structural simulation using a FETI-DP algorithm was awarded an ACM Gordon Bell prize already in 2002 using 4000 processors of the then second fastest supercomputer of the world. Unfortunately, the classical FETI-DP method does not scale well beyond 10K processor cores. Inexact FETI-DP methods, have shown a much better parallel scalability, and scalability for 65K cores was shown during the 2008 JUGENE scaling workshop in Jülich. Recently, nonlinear FETI-DP and BDDC methods with improved concurrency were introduced. In these methods, the nonlinear problem is decomposed into concurrent subproblems before linearisation. This is opposed to standard Newton-Krylov approaches where the problem is first linearised and then decomposed.

In the FE2TI computational scale bridging approach, in each macroscopic Gauß point a microscopic problem is solved using a FETI-DP method.